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Anomalous beam propagation in low index-contrast metamaterials has been analyzed. The condition for a well-collimated beam is found to be depending on the beam width and the pertinent Fourier component of the dielectric function. Guided by this condition, an ultra-compact metamaterial structure is designed to deflect a light beam at a wide angle. The structure is tolerant to structural parameter deviation and has a wide bandwidth.

Metamaterials have aroused wide spread interest in recent years [

Anomalous beam propagation in metamaterials can be traced back to early studies of photonic crystals in 1998 [

The anomalous propagation characteristics observed in these metamaterials originate from the underlying subwavelength structures. Related problems have been studied in various scenarios in other fields. Particularly, in X-ray diffraction study, a “dynamic theory” has been developed [

To overcome these issues originated from beam divergence, it is necessary to quantitatively study the beam divergence with varying structure parameters and seek approaches to minimize the beam divergence under the constraints of small index-contrast. To start, we note that in the X-ray theory, the beam is assumed to originate from a point source with a uniform angular intensity spectrum. Such an ideal simplification is not applicable to integrated optics applications where the input beam has a finite width. We have introduced a wavevector distribution function

(a)

A closer look of Figure

An ultra-compact 47.3° beam deflector (effectively a wide-angle waveguide bend). Inset indicates the output beam profile (solid curve) is well matched to the waveguide mode profile (dotted line).

Figure

Loss variation with (a) wavelength and (b) polymer index.

For practical implementation of this structure, each waveguide will be a channel waveguide composed of higher index polymer core and lower index polymer cladding, as shown in Figure

Schematic of an example device structure (side view, not drawn to scale).

In summary, the condition for achieving well-collimated beams in a metamaterial has been analyzed. Guided by this analysis, we have designed ultra-compact, wide-angle beam deflection devices that are significantly smaller than conventional polymer integrated photonic devices. The simulations also show that these devices have a wide bandwidth and are insensitive to fabrication tolerances. A wide range of polymers can be chosen to fabricate these structures. Such polymer photonic devices are attractive for their compact size, low cost and flexible form.

This work is supported in part by AFOSR Grant No. FA9550-08-1-0394.